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A semi-markovian process

Let us call the probability, for a person of age x and in status j at time 0, of being in status k at time t. can be obtained by solving the ``forward Kolmogorov equations'', which decompose interval into and .

Introducing the 4 transition forces:

one can write for example:

These 6 differential equations can also be written (8):


with :

Last equations, involving have been suppressed for simplicity. Two of the four equations are redundant, because . The system can therefore clearly be reduced to a set of two first order differential equations involving four forces and submatrix :


Nicolas Brouard
Tue Jun 6 00:15:46 DF 1995